This last result is clearly unexpected. A priori it would have been very difficult to find out that the non-autonomous
version of the Hietarinta equation (REF ) was in fact a particular
case of the \(_{1}D_{4}\)  equation (REF ),
since the first one arises from the triplet ()
without tetrahedron property,
whereas the latter one arises from the triplet (REF )
with tetrahedron property.
However, in general, a quad-equation can arise both from a sextuplet (triplet) with
or without the tetrahedron property since the tetrahedron property
is a property of the sextuplet \((\) triplet\()\)  of equations and not a property
of the equation itself.
Examples of this phenomenon were already known in literature
[1]}, [2]}, [3]}.
The example presented here is another one and it is rather non-trivial.
